Consider the particles in a gas centrifuge, a device used to separate particles of different mass by whirling them in a circular path of radius r at angular speed ω. The centripetal force acting on a particle is m_0*ω^2*r. (b) Show that the density of the particles as a function of r is n(r)=n_0 e^(m_0 r^2 ω^2/2k_B T).